This section features a case study that is inspired by
applications in machine learning [1]}, [2]}.
The classical Monge optimal transportation (OT) problem
deals with the construction of optimal
couplings for two given probability distributions. We explain how this problem, in its simplest version, can be written as a linear program (REF ). Many generalizations can be treated analogously; see e.g. [3]}, [4]}. In Subsection REF 
we carry this out for unbalanced OT.
